Question

In a right angled triangle ABC ,angle A is Acute , angle B=90° and tan A = 5/12 . Find i) cosA ii) cosec - cot A

Answer 1

tanA=opp/adj=5/12

=>hyp=√(opp²+adj²)

=√(25+144)=√169=13

1. cosA=adj/hyp=12/13
2. cosecA-cotA=13/5-12/5=1/5

Answer 2

Given:

Angle B=90° and tan A = 5/12

To find:

i) cosA

ii) cosec A- cot A

Solution:

The value of cos A is 12/13 and cosec A-cot A is 1/5.

We can determine the values by following the given steps-

We know that the given triangle is right-angled at B and angle A is acute.

We are given that tan A=5/12.

From trigonometry, tan A=perpendicular/base.

So, the perpendicular=5 units and the base=12 units.

Since the triangle is right-angled, the length of the hypoteuse=13 units as (5, 12, 13) is a Pythagorean triplet.

Now, we know that BC=5 units, AB=12 units and AC=13 units.

i) The value of cos A=Base/Hypotenuse

Cos A=AB/AC

Using the values,

Cos A=12/13

ii) Similarly, we will determine the value of cosec A-cot A.

We know that cosec A=1/sin A and cot A=1/tan A

So, sin A=perpendicular/hypotenuse

sin A=BC/AC

sin A=5/13

Cosec A=13/5

Cot A=12/5

Using the values, we get

Cosec A-Cot A=13/5-12/5

=(13-12)/5

=1/5

Therefore, the value of cos A is 12/13 and cosec A-cot A is 1/5.